Determination of the average lifetime of b-baryons

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P. Abreu, W. Adam, T. Adye, E. Agasi, I. Ajinenko, R. Aleksan, G D. Alekseev, R. Alemany, P P. Allport, U. Amaldi, et al.

To cite this version:

CERN{PPE/96-21

19 February 1996

Determination of the average

lifetime of

-baryons

DELPHI Collaboration

Abstract

The average lifetime of b-baryons has been studied using 3106 hadronic Z0

decays collected by the DELPHI detector at LEP. Three methods have been used, based on the measurement of dierent observables: the proper decay time distribution of 206 vertices reconstructed with a , a lepton and an oppositely charged pion; the impact parameter distribution of 441 muons with high trans-verse momentum accompanied by a  in the same jet; and the proper decay time distribution of 125 c-lepton decay vertices with the c exclusively

recon-structed through its pK, pK0 _{and 3 decay modes. The combined result}

is :

(b-baryon) = (1:25+0:13_0:11

0:04(syst)

+0:03_{0:05(syst)) ps}

where the rst systematic error is due to experimental uncertainties and the second to the uncertainties in the modelling of the b-baryon production and semi-leptonicdecay. Including the measurement recently published by DELPHI based on a sample of proton-muon vertices, the average b-baryon lifetime is :

(b-baryon) = (1:250:11(stat)0:05(syst)) ps.

P.Abreu , W.Adam , T.Adye , E.Agasi , I.Ajinenko , R.Aleksan , G.D.Alekseev , R.Alemany , P.P.Allport22, S.Almehed24, U.Amaldi9, S.Amato47, A.Andreazza28, M.L.Andrieux14, P.Antilogus9,

W-D.Apel17, Y.Arnoud39, B.Asman44, J-E.Augustin19, A.Augustinus9, P.Baillon9, P.Bambade19, F.Barao21,

R.Barate14, M.Barbi47, D.Y.Bardin16, A.Baroncelli40, O.Barring24, J.A.Barrio26, W.Bartl50, M.J.Bates37,

M.Battaglia15, M.Baubillier23, J.Baudot39, K-H.Becks52, M.Begalli6, P.Beilliere8, Yu.Belokopytov9;53,

K.Belous42, A.C.Benvenuti5, M.Berggren47, D.Bertrand2, F.Bianchi45, M.Bigi45, M.S.Bilenky16, P.Billoir23,

D.Bloch10, M.Blume52, S.Blyth35, T.Bolognese39, M.Bonesini28, W.Bonivento28, P.S.L.Booth22, G.Borisov42,

C.Bosio40, S.Bosworth35, O.Botner48, E.Boudinov31, B.Bouquet19, C.Bourdarios9, T.J.V.Bowcock22,

M.Bozzo13, P.Branchini40, K.D.Brand36, T.Brenke52, R.A.Brenner15, C.Bricman2, L.Brillault23, R.C.A.Brown9,

P.Bruckman18, J-M.Brunet8, L.Bugge33, T.Buran33, T.Burgsmueller52, P.Buschmann52, A.Buys9, S.Cabrera49,

M.Caccia28, M.Calvi28, A.J.Camacho Rozas41, T.Camporesi9, V.Canale38, M.Canepa13, K.Cankocak44, F.Cao2,

F.Carena9, L.Carroll22, C.Caso13, M.V.Castillo Gimenez49, A.Cattai9, F.R.Cavallo5, L.Cerrito38, V.Chabaud9,

M.Chapkin42, Ph.Charpentier9, L.Chaussard25, J.Chauveau23, P.Checchia36, G.A.Chelkov16, M.Chen2,

R.Chierici45, P.Chliapnikov42, P.Chochula7, V.Chorowicz9, J.Chudoba30, V.Cindro43, P.Collins9,

J.L.Contreras19, R.Contri13, E.Cortina49, G.Cosme19, F.Cossutti46, H.B.Crawley1, D.Crennell37, G.Crosetti13,

J.Cuevas Maestro34, S.Czellar15, E.Dahl-Jensen29, J.Dahm52, B.Dalmagne19, M.Dam29, G.Damgaard29,

P.D.Dauncey37, M.Davenport9, W.Da Silva23, C.Defoix8, A.Deghorain2, G.Della Ricca46, P.Delpierre27,

N.Demaria35, A.De Angelis9, W.De Boer17, S.De Brabandere2, C.De Clercq2, C.De La Vaissiere23,

B.De Lotto46, A.De Min36, L.De Paula47, C.De Saint-Jean39, H.Dijkstra9, L.Di Ciaccio38, F.Djama10,

J.Dolbeau8, M.Donszelmann9, K.Doroba51, M.Dracos10, J.Drees52, K.-A.Drees52, M.Dris32, Y.Dufour9,

D.Edsall1, R.Ehret17, G.Eigen4, T.Ekelof48, G.Ekspong44, M.Elsing52, J-P.Engel10, N.Ershaidat23, B.Erzen43,

E.Falk24, D.Fassouliotis32, M.Feindt9, A.Ferrer49, T.A.Filippas32, A.Firestone1, P.-A.Fischer10, H.Foeth9,

E.Fokitis32, F.Fontanelli13, F.Formenti9, B.Franek37, P.Frenkiel8, D.C.Fries17, A.G.Frodesen4, R.Fruhwirth50,

F.Fulda-Quenzer19, J.Fuster49, A.Galloni22, D.Gamba45, M.Gandelman6, C.Garcia49, J.Garcia41, C.Gaspar9,

U.Gasparini36, Ph.Gavillet9, E.N.Gazis32, D.Gele10, J-P.Gerber10, L.Gerdyukov42, M.Gibbs22, R.Gokieli51,

B.Golob43, G.Gopal37, L.Gorn1, M.Gorski51, Yu.Gouz45;53, V.Gracco13, E.Graziani40, G.Grosdidier19,

K.Grzelak51, S.Gumenyuk28;53, P.Gunnarsson44, M.Gunther48, J.Guy37, F.Hahn9, S.Hahn52, Z.Hajduk18,

A.Hallgren48, K.Hamacher52, W.Hao31, F.J.Harris35, V.Hedberg24, R.Henriques21, J.J.Hernandez49,

P.Herquet2, H.Herr9, T.L.Hessing35, E.Higon49, H.J.Hilke9, T.S.Hill1, S-O.Holmgren44, P.J.Holt35,

D.Holthuizen31, S.Hoorelbeke2, M.Houlden22, J.Hrubec50, K.Huet2, K.Hultqvist44, J.N.Jackson22,

R.Jacobsson44, P.Jalocha18, R.Janik7, Ch.Jarlskog24, G.Jarlskog24, P.Jarry39, B.Jean-Marie19,

E.K.Johansson44, L.Jonsson24, P.Jonsson24, C.Joram9, P.Juillot10, M.Kaiser17, F.Kapusta23, K.Karafasoulis11,

M.Karlsson44, E.Karvelas11, S.Katsanevas3, E.C.Katsous32, R.Keranen4, Yu.Khokhlov42, B.A.Khomenko16,

N.N.Khovanski16, B.King22, N.J.Kjaer29, H.Klein9, A.Klovning4, P.Kluit31, B.Koene31, P.Kokkinias11,

M.Koratzinos9, K.Korcyl18, C.Kourkoumelis3, O.Kouznetsov13;16, P.-H.Kramer52, M.Krammer50, C.Kreuter17,

I.Kronkvist24, Z.Krumstein16, W.Krupinski18, P.Kubinec7, W.Kucewicz18, K.Kurvinen15, C.Lacasta49,

I.Laktineh25, S.Lamblot23, J.W.Lamsa1, L.Lanceri46, D.W.Lane1, P.Langefeld52, I.Last22, J-P.Laugier39,

R.Lauhakangas15, G.Leder50, F.Ledroit14, V.Lefebure2, C.K.Legan1, R.Leitner30, Y.Lemoigne39, J.Lemonne2,

G.Lenzen52, V.Lepeltier19, T.Lesiak36, D.Liko50, R.Lindner52, A.Lipniacka36, I.Lippi36, B.Loerstad24,

J.G.Loken35, J.M.Lopez41, D.Loukas11, P.Lutz39, L.Lyons35, J.MacNaughton50, G.Maehlum17, A.Maio21,

V.Malychev16, F.Mandl50, J.Marco41, R.Marco41, B.Marechal47, M.Margoni36, J-C.Marin9, C.Mariotti40,

A.Markou11, T.Maron52, C.Martinez-Rivero41, F.Martinez-Vidal49, S.Marti i Garcia49, J.Masik30,

F.Matorras41, C.Matteuzzi9, G.Matthiae38, M.Mazzucato36, M.Mc Cubbin9, R.Mc Kay1, R.Mc Nulty22,

J.Medbo48, M.Merk31, C.Meroni28, S.Meyer17, W.T.Meyer1, M.Michelotto36, E.Migliore45, L.Mirabito25,

W.A.Mitaro50, U.Mjoernmark24, T.Moa44, R.Moeller29, K.Moenig9, M.R.Monge13, P.Morettini13,

H.Mueller17, L.M.Mundim6, W.J.Murray37, B.Muryn18, G.Myatt35, F.Naraghi14, F.L.Navarria5, S.Navas49,

K.Nawrocki51, P.Negri28, S.Nemecek12, W.Neumann52, N.Neumeister50, R.Nicolaidou3, B.S.Nielsen29,

M.Nieuwenhuizen31, V.Nikolaenko10, P.Niss44, A.Nomerotski36, A.Normand35, W.Oberschulte-Beckmann17,

V.Obraztsov42, A.G.Olshevski16, A.Onofre21, R.Orava15, K.Osterberg15, A.Ouraou39, P.Paganini19,

M.Paganoni9, P.Pages10, H.Palka18, Th.D.Papadopoulou3 2, K.Papageorgiou11, L.Pape9, C.Parkes35,

F.Parodi13, A.Passeri40, M.Pegoraro36, L.Peralta21, H.Pernegger50, A.Perrotta5, C.Petridou46, A.Petrolini13,

M.Petrovyck28;53, H.T.Phillips37, G.Piana13, F.Pierre39, M.Pimenta21, M.Pindo28, S.Plaszczynski19,

O.Podobrin17, M.E.Pol6, G.Polok18, P.Poropat46, V.Pozdniakov16, M.Prest46, P.Privitera38, N.Pukhaeva16,

A.Pullia28, D.Radojicic35, S.Ragazzi28, H.Rahmani32, P.N.Rato20, A.L.Read33, M.Reale52, P.Rebecchi19,

N.G.Redaelli28, M.Regler50, D.Reid9, P.B.Renton35, L.K.Resvanis3, F.Richard19, J.Richardson22, J.Ridky12,

G.Rinaudo45, I.Ripp39, A.Romero45, I.Roncagliolo13, P.Ronchese36, L.Roos14, E.I.Rosenberg1, E.Rosso9,

P.Roudeau19, T.Rovelli5, W.Ruckstuhl31, V.Ruhlmann-Kleider3 9, A.Ruiz41, K.Rybicki18, H.Saarikko15,

Y.Sacquin39, A.Sadovsky16, G.Sajot14, J.Salt49, J.Sanchez26, M.Sannino13, M.Schimmelpfennig17,

H.Schneider17, U.Schwickerath17, M.A.E.Schyns52, G.Sciolla45, F.Scuri46, P.Seager20, Y.Sedykh16, A.M.Segar35,

A.Seitz17, R.Sekulin37, R.C.Shellard6, I.Siccama31, P.Siegrist39, S.Simonetti39, F.Simonetto36, A.N.Sisakian16,

B.Sitar7, T.B.Skaali33, G.Smadja25, N.Smirnov42, O.Smirnova16, G.R.Smith37, O.Solovianov42, R.Sosnowski51,

D.Souza-Santos6, T.Spassov21, E.Spiriti40, P.Sponholz52, S.Squarcia13, C.Stanescu40, S.Stapnes33, I.Stavitski36,

A.Trombini , C.Troncon , A.Tsirou , M-L.Turluer , I.A.Tyapkin , M.Tyndel , S.Tzamarias , B.Ueberschaer52, O.Ullaland9, V.Uvarov42, G.Valenti5, E.Vallazza9, C.Vander Velde2, G.W.Van Apeldoorn31,

P.Van Dam31, W.K.Van Doninck2, J.Van Eldik31, N.Vassilopoulos35, G.Vegni28, L.Ventura36, W.Venus37,

F.Verbeure2, M.Verlato36, L.S.Vertogradov16, D.Vilanova39, P.Vincent25, L.Vitale46, E.Vlasov42,

A.S.Vodopyanov16, V.Vrba12, H.Wahlen52, C.Walck44, F.Waldner46, M.Weierstall52, P.Weilhammer9,

C.Weiser17, A.M.Wetherell9, D.Wicke52, J.H.Wickens2, M.Wielers17, G.R.Wilkinson35, W.S.C.Williams35,

M.Winter10, M.Witek18, K.Woschnagg48, K.Yip35, O.Yushchenko42, F.Zach25, A.Zaitsev42, A.Zalewska18,

P.Zalewski51, D.Zavrtanik43, E.Zevgolatakos11, N.I.Zimin16, M.Zito39, D.Zontar43, R.Zuberi35, G.C.Zucchelli44,

G.Zumerle36

1Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA 2Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium

and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium

and Faculte des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium

3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece 4Department of Physics, University of Bergen, Allegaten 55, N-5007 Bergen, Norway

5Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy 6Centro Brasileiro de Pesquisas Fisicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil

and Depto. de Fisica, Pont. Univ. Catolica, C.P. 38071 RJ-22453 Rio de Janeiro, Brazil

and Inst. de Fisica, Univ. Estadual do Rio de Janeiro, rua S~ao Francisco Xavier 524, Rio de Janeiro, Brazil

7Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 Bratislava, Slovakia 8College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France 9CERN, CH-1211 Geneva 23, Switzerland

10Centre de Recherche Nucleaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France 11Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece

12FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic 13Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy

14Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, F-38026 Grenoble Cedex, France 15Research Institute for High Energy Physics, SEFT, P.O. Box 9, FIN-00014 Helsinki, Finland

16Joint Institute for Nuclear Research, Dubna, Head Post Oce, P.O. Box 79, 101 000 Moscow, Russian Federation 17Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany 18Institute of Nuclear Physics and University of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland 19Universite de Paris-Sud, Lab. de l'Accelerateur Lineaire, IN2P3-CNRS, B^at. 200, F-91405 Orsay Cedex, France 20School of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK

21LIP, IST, FCUL - Av. Elias Garcia, 14-1o, P-1000 Lisboa Codex, Portugal

22Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK

23LPNHE, IN2P3-CNRS, Universites Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France 24Department of Physics, University of Lund, Solvegatan 14, S-22363 Lund, Sweden

25Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France 26Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain

27Univ. d'Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France 28Dipartimento di Fisica, Universita di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy 29Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark

30NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic 31NIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands

32National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece 33Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway

34Dpto. Fisica, Univ. Oviedo, C/P. Perez Casas, S/N-33006 Oviedo, Spain 35Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

36Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy 37Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK

38Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy 39Centre d'Etudes de Saclay, DSM/DAPNIA, F-91191 Gif-sur-Yvette Cedex, France

40Istituto Superiore di Sanita, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy

41Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros, S/N-39006 Santander, Spain, (CICYT-AEN93-0832) 42Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation

43J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljana, Slovenia 44Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden

45Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy 46Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italy

and Istituto di Fisica, Universita di Udine, I-33100 Udine, Italy

47Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fund~ao BR-21945-970 Rio de Janeiro, Brazil 48Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden

49IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain 50Institut fur Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria 51Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland

1 Introduction

Baryons containing a beauty quark, referred to as b-baryons throughout this paper, were rst observed by the UA1 and SFM experiments, which reported signals for the exclusive b decays into J=  [1] and pD0 and +c + [2] respectively. At LEP,

evidence forb-baryon production in Z0 _{hadronic decays was found [3,4] in the correlation}

observed between 's or c's and leptons (`'s). Using this correlation, rst measurements

of the averageb-baryon lifetime were made [4,5]. It is predicted to be shorter than that of B mesons, but only by some (5 10)% [6]. But current experimental data [7,8] indicate a substantially shorter lifetime that would be dicult to accommodate theoretically. It is therefore important to pursue these measurements further.

This paper updates the recent DELPHI results on the average lifetime of b-baryons based on the proper timedistribution of partially reconstructedb-baryon decay candidates containing a  or a c correlated with a lepton [8]. The c !pKo and c !3 decay

modes are added to the c !pK mode previously used in the exclusive reconstruction

of c particles, an analysis based on the the impact parameter distribution of muons in

the same jet as a  is also added, and the data collected in 1994 are included.

2 The DELPHI Detector

The DELPHI detector and its performance have been described in detail elsewhere [9,10]. Both the charged particle tracking through the uniform axial eld and the particle identication are important in this analysis. The detector elements used for tracking are the Vertex Detector (VD), the Inner Detector (ID), the Time Projection Chamber (TPC) and the Outer Detector (OD). The VD provides the high precision needed near the primary vertex. Hadron identication is based mainly on the Ring Imaging Cherenkov de-tector (RICH), and lepton identication on the barrel electromagnetic calorimeter (HPC) and the muon chambers; supplementary information is provided by the ionisation loss measurements in the TPC.

For the data taken from 1991 to 1993, the VD consisted of 3 cylindrical layers of silicon detectors (radii 6.3, 9.0 and 10.9 cm) measuring points in the plane transverse to the beam direction (r coordinate) in the polar angle range 43 <  < 137. In 1994,

two layers were equipped with detector modules with double sided readout providing a single hit precision of 7.6 m in the r coordinate, similar to that obtained previously, and 9 m in the coordinate parallel to the beam (z) [11]. For high momentum tracks with associated hits in the VD, the extrapolation precision close to the interaction region was 20 m in the r plane and 34 m in the rz plane.

Charged particle tracks were reconstructed with 95% eciency and with a momentum resolution p=p < 2:010 3p (GeV/c) in the polar angle region 25

 <  < 155. The

primary vertex of the e+_{e interaction was reconstructed on an event-by-event basis}

using a beam spot constraint. The position of the primary vertex could be determined in this way [10] to a precision of about 40m (slightly dependent on the avour of the primaryquark-antiquark pair) in the plane transverse to the beam direction. In this plane, secondary vertices from beauty and charm decays were reconstructed with a precision of about 300 m along the ight direction of the decaying particle.

16 and 30 GeV/c in the same way, and also provided proton selection in the intermediate 8{16 GeV/c momentum range, where protons gave no Cherenkov light, by vetoing pions and kaons. The dE=dx measurement had a precision of 7% in the momentum range

4< p < 25 GeV/c.

The barrel electromagnetic calorimeter (HPC) covered the polar angle region 46 <  < 134 and detected electrons with an energy precision

E=E = 0:040:33= p

E (E in GeV). Two layers of muon chambers covered the polar angle region 20 <  < 160,

except for two regions of 3

 around  = 42 and  = 138. The rst layer consisted of

three planes of chambers and was inside the return yoke of the magnet, after 90 cm of iron, while the second, with two chamber planes, was mounted outside the yoke, behind a further 20 cm of iron.

3 Hadronic

selection and particle identication

Hadronic events from Z0 _{decays were selected by requiring a charged multiplicity}

greater than 4 and a total reconstructed energy greater than 0.12p

s, where p

s is the centre of mass energy; charged particles were required to have a momentum greater than 0.4 GeV/c and a polar angle between 20 and 160. The overall trigger and selection

e-ciency was 0:95000:0011 [13]. An identied lepton was required in the event; only tracks

with momentum bigger than 3 GeV/c were considered as possible lepton candidates. Lepton identication in the DELPHI detector is described in [10]. The probability of a track being an electron was calculated using a) the spatial separation between its extrapolated position at the HPC and the position of the nearest electromagnetic shower, b) a comparison between its momentum and the measured energy, and c) a successful t to the longitudinal prole of the shower in the 9 HPC layers. ThedE=dx measurement in the TPC was used in the algorithm as independent and complementaryinformation. With the selections applied, the electron identication eciency inside the angular acceptance of the HPC was found to be (651)% and the hadron misidentication probability 0:4%.

The probability of a track being a muon was calculated from a global 2 _{of the match}

between its extrapolation to the muon chambers and the hits observed there. With the selections applied, the muon identication eciency was (861)% and the hadron

misidentication probability (0:70:1)%.

Hadron identication in the DELPHI detector is also described in [10]. The analysis presented in this paper used protons in a momentum range well above the pion threshold in the gas radiator of 2.5 GeV/c. Above this threshold, the gas radiator vetoed pions up to 16 GeV/c. The average proton selection eciency was 75% (varying slightly with the momentum) for a pion rejection factor of 15. Kaons were vetoed in the same way between 8.5 GeV/c, the gas radiator threshold for kaons, and 16 GeV/c. Above 16 GeV/c, identication was provided by the measurement of the Cherenkov angle of the detected photons [10,14], with (8010)% eciency and rejection factors of 5-10. The algorithms

were also applied to the liquid radiator data, which provided complementary information for K= and K=p separation in the momentum range 1-7 GeV/c.

4

and

reconstruction

 particles were used in the -lepton analyses and in the reconstruction of the c !3 decay mode in the c-lepton analysis. K0 mesons were used to reconstruct

the c !pK

The !p and K0 ! decays were reconstructed if the distance in the r plane

between the  decay point and primary vertex was less than 90cm. This condition meant that the decay products had track segments at least 20cm long in the TPC. The reconstruction of two-prong decays in the DELPHI detector is described in detail in [10]. In addition to the selection criteria dened there, the  selection required a loose particle identication for the decay product of higher momentum, assumed to be the proton: the  candidate was retained if the proton candidate had a measured dE=dx at least one standard deviation below the value expected for the pion hypothesis or was tagged as a proton by the RICH. For  particles with a momentum above 4 GeV/c, this requirement reduced the combinatorial background by about a factor of two, with negligible eciency loss. The eciencies for the decay modes considered varied between 35% and 10% in the =K0 _{momentum range 2-20 GeV/c.}

The invariant mass plots for accepted  andK0 _{candidates withp > 4 GeV/c}

accom-panied by a lepton withp > 3 GeV/c in the same hemisphere (dened by the thrust axis) are shown in Figs. 1a,b respectively.

5 Lifetime measurements using

pairs

Decays of b-baryons giving a -lepton (`) pair in the nal state are thought to originate mainly fromb-baryon decays into c`X with c !X

0, where X and X0 are

any particles. Typically, the lepton has high transverse momentum,pT, with respect to

the jet direction, dened below, and also high longitudinal momentum. Also, the  has a harder momentum spectrum than the 's produced in light quark fragmentation. In the following, the selection of the ` pairs required the momentum of the candidate to be greater than 4 GeV/c and the momentum of the lepton to be greater than 3 GeV/c.

Background sources of ` in the same jet were:

- B meson semileptonic decays such as B !c N` X (where N is an antibaryon),

- c semileptonic decays

- accidental correlations of a  candidate and a lepton.

In both b-baryon and B meson decays, the proton from the  decay has the opposite sign to the lepton, i.e. the pairs are p` not p`+ _{(charged conjugate states are always}

implied throughout this paper). This combination is referred to as right sign. However,

the contribution of semileptonicB meson decays has been estimated to be negligible [8]. Background events from directc production through the c!c !`X decay chain

have protons and leptons of the same sign (referred to as wrongsign combinations in the

following); but the lepton pT spectrum is softer, so this background was reduced to a

negligible amount by the pT and ` invariant mass cuts dened below.

Two methods using ` pairs were developed for the determination of the average b-baryon lifetime. The rst one was based on the reconstruction of b-baryon candidate decay vertices using the , the lepton (e or ) and an additional track supposed to come from the b-baryon decay chain. The proper time distribution of these candidate vertices was tted. The second method used only the events with a  and a muon and was based on the impact parameter distribution of the muons.

5.1 The proper time distribution analysis

described below. Charged and neutral particles were clustered into jets using the LUND jet nding algorithm LUCLUS [15] with a clustering mass parameter equal to 2.5 GeV/c2_.

The lepton was accepted if its pT, computed including the lepton in the jet (pinT), was

greater than 0.6 GeV/c. The ` pair was required to have an invariant mass in the range 2.0 to 4.5 GeV/c2 _{and a total momentum greater than 9 GeV/c.}

The determination of the average b-baryon lifetime was based on the reconstruction of the decay vertex and hence the decay length. Since the extrapolation of the  ight direction to the interaction region was not precise enough to separate secondary from tertiary vertices in theb-baryon decay chain, a unique secondary vertex was reconstructed using the , the correlated high pT lepton and an oppositely charged particle (assumed

to be a pion) with momentum greater than 0.5 GeV/c. The 2 _{probability of the vertex}

t was required to be greater than 0.001. The lepton and the candidate pion were each required to have at least two associated hits in the vertex detector. To reduce the combinatorial background, the (`) invariant mass had to be less than 5.8 GeV/c2 _and

the () invariant mass less than 2.3 GeV/c2_{. If more than one pion gave a vertex which}

passed the above cuts, the highest momentum one was chosen. In the simulation, in 90% of the cases the candidate pion associated to the vertex did originate from the b decay

chain. Out of 532 (280) right sign (wrong sign) ` events with 1:106 < M(p) < 1:130 GeV/c2_{, 206 (113) decay vertices were reconstructed. The corresponding (p) invariant}

mass plots are shown in Figs. 2a,c respectively.

The b-baryon purity of the sample after the vertex reconstruction, Fs, was

deter-mined from the data by a t to the mass plots for the right and wrong sign correlations (Figs. 2a,c). In the simulation, the background from a true  accidentally accompanied by a lepton was found to be (83)% bigger in the wrong sign sample than in the right sign

sample. This asymmetry was due to the contribution from events with both a b-baryon and a  from the primary interaction in the same jet, in which the b-baryon decayed semileptonically and the  was reconstructed. Taking into account this dierence and assuming the number of background events from all the other sources of accidental com-binations to be the same in both samples, as predicted by the simulation, the b-baryon purity of the signal sample was found to be Fs = (555)%.

After the selection described above, background events were dominated by accidental combinations of a  candidate (either a true  from the primary vertex or a fake ) and a lepton candidate (mostly true leptons). They contained fake vertices constructed using charged tracks from the primary vertex only, and also vertices using tracks originating from charm and B meson decays. The time distribution of the former component (the

\non- ying background") was parametrised by two Gaussian functions centred on zero

with widths determined by the detector resolution. The fraction of the total background, Ffb, due to the latter component (the \ ying background") and its average lifetime were

determined from the data by the tting procedure described below. The fraction of the background due to the non- ying component, Fnf, was then determined by the

normali-sation equation : Ffb+Fnf = 1.

The b-baryon momentum was estimated using the residual energy technique. The

residual energy,Eres, was computed by subtracting the energies of the ,E, the lepton,

E`, and the pion, E, from the total \visible" energy, Evis, in the hemisphere, dened

by the plane perpendicular to the total momentum ptot of those three particles, that

from the equation :

Eb =Ebeam Eres =Ebeam Evis+E+E`+E

whereEbeam is the beam energy. This method of estimating theb-baryon energy assumes

that all the unobserved energy is due to particles from theb-baryon decay and that all the residual energy is due to particles not from theb-baryon; this holds for the decay b-baryon

!` if only the energy of the neutrino is undetected. In the simulation an additional

small correction (a factor 0:97 for unpolarised b-baryons) is needed to reproduce the generated spectrum [8]. This correction factor was therefore applied to the above value of Ei. The momentumpb of theb-baryon was then deduced.

The correlation between the reconstructed and generated b-baryon energy and the resolution of the b-baryon momentum are shown in Figs. 3a,b for a sample of simulated b-baryon ! cl decays. A Gaussian t to the distribution in Fig. 3b gave a fractional

b-baryon momentumerror p=p = 0:14; if additional pions were generated in the b-baryon

semileptonic decay the resolution deteriorated to 18% and the correction factor increased. This eect was taken into account in the systematic errors, as discussed below.

A maximum likelihood t was performed simultaneously to the lifetime distribution of the 206 events of the signal sample and to the 113 background vertices with the wrong sign which survived the same selection procedure as that used for the signal. The likelihood function f was dened as the sum of two exponential functions representing the time distributions of the signal and the ying background, each convoluted with a Gaussian function representing the experimental resolution, and a double Gaussian term representing the behaviour of the non- ying background. Thus the function to be maximised was L = iln[f(ti;i;;bck;Ffb)]; with f(ti;i;;bck;Ffb) =Fs
E()G(i) + (1 Fs)
[Ffb
E(bck)G(i) + (1 Ffb)
((1 )
G(i) +
G(ki))] whereE(x) = 1

xexp( ti=x) is a decreasing exponential with average x;  and bck are the

signal and background lifetimes; andG(i) represents a Gaussian resolution function with

standard deviation i where i is the error on the proper decay time ti. The constants

and k described the size and width of the second Gaussian describing the tail in the detector resolution distribution. They were xed to the values 0.06 and 4.7 respectively, obtained in the simulation from a double Gaussian t to the pull distribution for the reconstructed position of the b-baryon vertex shown in Fig. 3c. The decay time ti was

computed from the formula ti = (li=sini)=(pi=Mbar), where li is the measured decay

length in the plane transverse to the beam direction, i is the polar angle of the total

momentumvectorptot,piis theb-baryon momentumpb estimated by the residual energy

technique described above, andMbar is the assumedb-baryon mass. The systematic error

associated with thei computation and the parametrisation of the non- ying background

will be discussed below. The normalisation constant Fs for the signal fraction was xed

to the tted value of the b-baryon purity discussed above in the right sign sample and was dened to be zero in the wrong sign sample. A three parameter t to the data gave

(b-baryon)= 1:46+0:22_{0:21 ps}

with a background lifetimebck = 1:37+0:210:18 ps and Ffb = 0:570:05. The result of the

t for the lifetime was stable within 0:03 ps when changing the pT cut on the lepton

Table 1: Correlation matrix between the variables of the lifetime t to the proper ight time distribution of ` vertices.

 bck Ffb

 1:00

bck 0:46 1:00

Ffb 0:02 0:25 1:00

0.62) and within 0:09 ps when changing the minimum accepted b-baryon energy from 15 to 40 GeV/c2_{. The lifetime distributions for the signal events and for the background,}

together with the probability functions resulting from the t, are shown in Figs. 2b,d. The correlation matrix is shown in Table 1, where the anticorrelation between the signal and background lifetimes is quantied.

Figs. 4a and 4b compare the distributions of the reconstructed lifetimein the data with the corresponding distributions in the simulation, obtained by applying the same recon-struction and selection procedure as in the data to about 5 million simulatedZ0 _hadronic

decays. The DELPHI simulation program used the JETSET Parton Shower event gener-ator [16], with a b-baryon production rate reproducing the experimentally observed rate [8]. In the simulation, the generated lifetime of all weakly decayingb-baryons was 1.3 ps. The parts of the distributions for negative reconstructed ight time, which are sensitive to the behaviour of the detector resolution which was xed from the simulation in the likelihood t, show good agreement between real and simulated data.

To check the consistency of the method, the same analysis and tting procedure was applied to the simulated event sample, containing about 200 reconstructedb-baryon de-cays. The result was (b-baryon)= 1:36  0:12 ps and bck = 1:54  0:13 ps, with a

b-baryon purity Fs= (615)% and a tted ying background fractionFfb= 0:760:03.

This fraction correctly reproduced within the statistical error the fraction (0.75) of recon-structed decays in the simulated background sample in which at least one track originated from a weakly decaying particle.

The dierent contributions to the systematic uncertainty are listed in Table 2. The rst one re ects the uncertainty in the signal purity, which was estimated from the ts to the right and wrong sign  mass peaks to be 0:55 0:05. The second one comes

from the estimation of the errori on the individual time measurements discussed below.

The third is due to the possible bias introduced by the t procedure. The remaining contributions aect the estimation of the b-baryon momentum.

The error i was assumed to be Gaussian and estimated as :

i =ti
q

(il=li)2 + (p=p)2 + (sin=sin)2

whereil is the error on the decay lengthli, and p=p = 0:14 and sin=sin = 0:025 are the

resolutions on the estimatedb-baryon momentum and direction found in the simulation. The error on the secondary vertex position in the simulation resulting from the vertex t had to be scaled by a factor 1.5 to reproduce the observed spread of the dierence between the reconstructed and generated decay lengths, as determined from the pull distribution of Fig. 3c. This rescaling, which was also used in the real data, changed the result for the ttedb-baryon lifetime by 0:03 ps both in the real data and in the simulation. Varying the resolution on the b-baryon momentum in the range (14 18)% to take into account the eect onp=p of additional hadrons (other than the c) in theb-baryon semi-leptonic

Table 2: Contributions to the systematic error on the averageb-baryon lifetime measured using the proper time distribution of ` vertices: the modelling uncertainties in the lower part of the table are fully correlated with corresponding errors in other analyses.

Error source Range of Variation Syst. error (ps) Signal Fraction Fs 0:550:05 0:01

i Parametrisation see text 0:04

Fit procedure bias see text 0:05

c Decay Mode Uncertainty one st. dev. [17] 0:02

< Eb > =Ebeam 0:70 0:03 0:01 Mbar 567070 MeV 0:015 (!) = exp[aIW(1 !)] aIW = 1:7+3:31:7 0:01 b polarisation 0:470:47 0:01 Br(b !c`n)=Br(b !c`) 0!0:3 0:06

Total systematic error +0:07_0:09

second Gaussian component of the non- ying background in the range 0 0:10 changed the tted b-baryon lifetime by 0:005 ps. An overall0:04 ps contribution to the total

systematic error was conservatively associated to the i estimation.

To control the possible bias introduced by the tting procedure, a t to about 600 reconstructed b-baryon decays from a dedicated simulation sample of 30000 b ! cl

decays generated with a lifetime of 1.30 ps gave (b-baryon)= 1:28 0:05 ps. The

statistical error of this result was considered as a systematic error from this possible error source.

The eect of the cdecay mode uncertainty was computed in the simulation by varying

within their experimental errors the relative amounts of the c ! , c ! o and

c !3 branching fractions [17]. The average value of the b-baryon energy, < E b >,

resulting from the fragmentation of theb-quark was assumed to be the same as the average value measured for b hadrons [18], with an uncertainty increased by a factor of 3 to take into account possible dierences betweenb-baryon and B-meson fragmentation. Varying it by the quoted uncertainty changed the correction factor in the b-baryon momentum estimation by0:7%. The assumed value of the average b-baryon mass, Mbar, was shifted

by 30 MeV/c2_{with respect to the measuredmass of the b,M(b) = 5640}50 MeV/c2[1],

to take into account the contribution of b production (measured to be 5 times smaller

than b production [19]), as the b mass is expected to be 25050 MeV/c

2 _{higher than}

the b mass. The b-baryon semileptonic decay was simulated in the framework of Heavy

Quark Eective Theory, using the Isgur-Wise function(!) = exp[aIW(1 !)][20], where

! = vb
v

c and v b (v

c) is the b-baryon (c-baryon) 4-velocity. The b polarisation

systematic was evaluated following the recommendations of [21]. If resonant and non-resonant b!c` + n decays are an important fraction of the total decay width,

where n is a positive integer, the b-baryon momentum estimation by the residual energy method must be further corrected. If the b semi-leptonic decay was assumed to be a

4 or 5 body decay in 30% of the cases, the tted lifetime was shifted by -0.06 ps with respect to the value obtained for the b !c` decay mode.

5.2 The muon impact parameter distribution analysis

In this analysis, only a  and a muon were reconstructed and theb-baryon lifetime was measured from the impact parameter distribution of the muons. Electron candidates were not used as bremsstrahlung radiation resulting from their passage through the detector material gave larger uncertainties in their impact parameters.

The muon candidates used were required to have at least two associated hits in the vertex detector, a momentum between 3 and 30 GeV/c, and a transverse momentum (pinT), dened as in the analysis described above, between 1 and 4 GeV/c. The  was required only to have a momentum above 4 GeV/c and a direction within 45 of the

muon. The distributions of the  mass for the right sign and wrong sign  candidates are shown in Figs. 5a,b. To be used in the lifetime analysis, the  mass was required to lie between 1.104 and 1.128 GeV/c2_{. A t to the mass peak and background, as shown}

in the gure, gave the number of right sign events above background as 30821 out of a

total of 441 events. The wrong sign sample gave 18619 out of 323 events. Correcting

for the (83)% asymmetry in the background combinations described previously, and for

a contribution of similar size where the muon is from charm decay, theb-baryon signal in the right sign sample was estimated to be 16930 events. This error estimate includes

a contribution from varying the parametrisation used in the mass t. This corresponds to a signal fraction, Fs, of 0:380:07.

The lifetime of the b-baryons was estimated from the impact parameter distribution of the muon candidates satisfying the above requirements. The impact parameters, , of the muons were calculated relative to an average beamspot, determined from several hundred events recorded close in time to the b-baryon candidate event. The impact parameters were assigned a \lifetime-sign" [10], determined by whether the track crosses its associated jet axis in front of (positive sign) or behind (negative sign) the beamspot. Particles resulting from the decay of ab-baryon with a ight path along the jet axis would be expected to have only positive lifetime-signed impact parameters, in the absence of resolution eects.

The contribution of the b-baryon to the muon impact parameter distribution was represented by a \physics function", which described the distribution expected in the absence of detector resolution eects. This was parametrised as a function of theb-baryon lifetime and was then convoluted with a \resolution function" to represent the beamspot size and the eects of the detector. The contribution not from b-baryon !X decays

was described by a \background function" parametrising the behaviour ofb!, b !c!

, c! , and fake lepton and  events. The relative proportions of these backgrounds

were taken from the simulation, with only the mean b hadron lifetime and the impact parameter distribution of the fake leptons being tted to the data, as described below. This background contribution was also convoluted with the resolution function. The sum of all expected contributions was then tted to the data using a maximumlikelihood technique to determine theb-baryon lifetime. The estimation of each of these components is described brie y below; full details of this analysis can be found in [22].

also calculated, again using a weighting technique to mimic dierent polarisation values. The uncertainty of the exponential parameters due to the uncertainty in the polarisation was considered as a separate source of systematic error, see Table 3.

The resolution function was determined directly from the data using a sample dom-inated by tracks from the primary vertex, where the width of the impact parameter distribution is due mainly to resolution eects. The above cuts were applied except that all muon identication requirements were removed, which reduced theb and c quark frac-tions in the sample. To further reduce these fracfrac-tions, the b-tagging variable dened in [10], PH, based on impact parameters, was calculated using the tracks in the hemisphere

opposite to the b-baryon candidate. The construction of PH was tuned [23] for both data

and simulation to have a at distribution over the range 0 < PH < 1 if all the tracks

considered came from a single vertex, and to be shifted to lower values if they did not. To select events for the resolution function determination, PH was required to satisfy

log10PH < 0:5 (i.e. PH > 0:316), preferentially removing b and c quark events. It

was estimated from the simulation that, in the resulting track sample, only 8% of tracks originated from decays of particles with non-zero lifetimes. The distribution of impact parameters divided by their errors for this sample was tted using two Gaussian functions over various impact parameter ranges between 0:02 cm and 0:10 cm. The narrower

of the two Gaussian functions described between 91% and 97% of the tracks and had a width,k1, in all cases equal to one within a few percent. The wider Gaussian described a

combination of the tail in the detector resolution distribution and the remaining non-zero lifetime component of the tracks; its width, k2, varied between 2.5 and 4.0. The widths

k1 andk2 were used to scale the impact parameter errors from their nominal values in the

likelihood function described below. The variation in the t parameters with the tted range was taken to re ect the uncertainty in the proportions of these two components. The systematic error associated to the parametrisation of the resolution function was 0.03 ps.

The background distribution was due to two main sources: the ying and non- ying backgrounds, as in the previous analysis. The biggest contribution,Ffb = 81%, was due to

muons from b and c hadron decays. These result from decays of particles with non-zero lifetimes and their expected impact parameter distribution was parametrised directly from the simulation, again using four-fold exponential distributions as for the physics function described above. In this case, the parametrisation was done as a function of the mean b hadron lifetime, with the c hadron lifetimes xed. The lifetime to be used for this component of the background function was estimated from the data by removing all  selection requirements from the right sign sample. This method was used, rather than tting the wrong sign sample as in the previous analysis, because it provides a much larger sample (it could not be used in the previous analysis as the  was needed to form the vertex). The muon sample was then reasonably insensitive to the b-baryon lifetime as it was dominated by B meson decays { less than 10% of the muons were expected to originate fromb-baryons. The background function was convoluted with the resolution function and used in the maximum likelihood t (see below) with the signal fraction,Fs, set to zero, to determine the meanb hadron lifetime of the background. The

resulting value was 1:6390:013+0:060:04 ps; the distribution and t are shown in Fig. 6a.

The remaining 19% of the background was from hadrons misidentied as muons, some of which originated from particles with signicant lifetimes. The impact parameter dis-tribution of this sample was measured from the data by removing the muon identication requirements, as for the resolution function study, but without imposing the opposite hemisphere PH cut. The resulting sample was found to have a mean impact parameter

of 52m, re ecting its lifetime component, and this sample was also parametrised by a four-fold exponential, as for the physics function.

A maximum likelihood t was performed to the 441 right sign events within the mass window specied above. The function to be maximised was the sum of the above contri-butions all convoluted with the resolution function:

L = iln[f(i;i;;bck)]; with f(i;i;;bck) = [Fs
E4() + (1 Fs)
(Ffb
E 0 4(bck) + (1 Ffb)
E 00 4)] [(1 )
G(k1i) +
G(k2i)]

where  is the b-baryon lifetime, E4 is the four-fold exponential for the muons from

b-baryons, E0

4 is the one for muons fromb and c background processes and E00

4 is for fake

muons from misidentied hadrons. The scaling factors k1;2 describe the narrow and wide

components respectively of the resolution function, while is the fraction in the wide Gaussian. The proportions of the physics and ying background functions, Fs and Ffb,

were xed and theb hadron lifetime in the background function, bck, was set to the value

deduced from the background t described above. The only remaining parameter was the b-baryon lifetime; the resulting value was:

(b-baryon)= 1:10+0:19_{0:17 ps}

where the error re ects the statistical contribution only. The distribution of impact parameters and the result of the t are shown in Fig. 6b.

The dierent contributions to the systematic uncertainty are listed in table 3. The rst re ects the uncertainty in the signal purity, which was estimated from the ts to the right sign and wrong sign  mass peaks described above. The second error arises from the nite simulation statistics used to parametrise the physics function. The next two errors are from the background and resolution function uncertainties. The main contribution to the background uncertainty was due to the eective background lifetime, in particular its systematic uncertainty. The uncertainty in the resolution function was estimated by varying the function t range between0:02 cm and 0:10 cm, as described above. The

remaining systematic errors listed in the table result from uncertainties in the description of theb-baryon properties, as considered in the previous analysis (see table 2). Summing the systematic uncertainties listed in table 3 in quadrature gives an overall systematic uncertainty of 0:09 ps.

6 Lifetime measurement using

pairs

The third analysis presented in this paper used fully reconstructed c ! pK,

c !K0p and c ! 3 decays correlated with an ` . Possible sources of c` in

the same jet were:

Table 3: Contributions to the systematic error on the averageb-baryon lifetime measured using muon impact parameters.

Error source Range of Variation Syst. error (ps) Signal Fraction Fs 0:380:07

+0:04_0:03

Physics Function see text 0:02

Background Lifetime 1:64+0:06_{0:04 ps} +0:04_0:05

Resolution Function see text 0:03

< Eb > and Mbar see table 2

0:02

b polarisation 0:470:47 0:05

Br(b !c`n)=Br(b !c`) 0!0:3 0:03

Total systematic error +0:09_0:09

- B meson semileptonic decays

- accidental correlations of a c candidate with a lepton or a fake lepton.

The c` combinations from b decays were characterised by higher invariant mass and

by higher transverse and longitudinal momentumof the lepton than the background pairs from other sources.

6.1 Selection of

! pK

decays

c candidates were selected by requiring :

- the proton momentum to be greater than the pion momentum, - the total momentum to be at least 10 GeV/c,

- the angle between the total momentum of the c candidate and the ight direction,

dened as the line from the primary vertex to the c vertex, to be below 90,

- the proton and the kaon to be tagged by the RICH.

If the RICH information was not available, the dE=dx measurement in the TPC for the proton candidate was required to be not more than 1 standard deviation above the expectation for a proton and thedE=dx measurementfor the kaon candidate was required to be within 2 standard deviations of the value expected for a kaon.

6.2 Selection of

! pK0

decays

In the reconstruction of this decay mode, the K0 _{candidates shown in Fig. 1b with}

invariant mass 0:480 < M() < 0:515 GeV/c2 _{were used. The candidate proton track}

had to be uniquely identied by the RICH (i.e. the kaon hypothesis had to be excluded by the identication algorithm). To reduce the combinatorial background further, the proton track and the lepton track accompanying the K0 _{candidate had to have at least}

two hits in the vertex detector and to t a common decay vertex with \positive" decay length, i.e. the scalar product of the ight direction and the total momentumptot of the

pK0_{-lepton system had to be positive. Also, the projected angle in the plane transverse}

to the beam direction between the ight direction and ptot had to be below 10.

6.3 Selection of

! 3

decays

The  candidates shown in Fig. 1a with invariant mass 1:105 < M(p) < 1:125 GeV/c2

tted using tracks with total electric charge equal to the proton charge in the  candidate. Again the vertex had to have positive decay length and the angle between the ight direction and the total momentum of the c candidate had to be less than 10.

6.4

c

-lepton selection and lifetime determination

The c candidates were paired with identied leptons of momentum over 3 GeV/c,

within a cone of 45 around the 

c direction. The lepton had to have a transverse

momentumwith respect to the jet axis, again computed including the lepton itself, greater than 0.6 GeV/c. The total momentum of the lepton and the c had to exceed 18 GeV/c

and the invariant mass of the c (ce) pair was required to be greater than 3.5 GeV/c2

(3.2 GeV/c2_).

The mass plots for the c candidates are shown in Figs. 7a-c for the three channels

considered. The full line (dashed line) histograms are the right sign (wrong sign) entries. The three channels are shown combined in Fig. 7d.

The b-baryon candidate vertices were reconstructed using the trajectories of the c

and the lepton to t a common vertex. In the c !pK0 case, thep-lepton vertex dened

in the c selection was used as b-baryon candidate vertex. The b-baryon momentum was

estimated with the residual energy technique:

Eb =Ebeam Eres =Ebeam Evis+E c +E`

with the quantities dened as in Sect. 5.1. In this case the simulation showed that, due to detector ineciencies, the b-baryon energy estimate had to be scaled by the factor 0:9500:015, where the quoted error was due to the nite simulation statistics available.

This error was included in the systematic errors. If one or two additional pions were produced in the b-baryon decay, the b-baryon energy was on average respectively 3.5 or 6 GeV too low. But as the selection eciency was lower for the multiple pion modes than for the mode with no additional pions, the eect of this uncertainty on the momentum resolution was found to be small.

A sample of 125 signal vertices was selected using right sign pairs with 2:250 < M(c)< 2:310 GeV/c2. In a similar way, a background sample of 139 vertices

was dened using wrong sign pairs with 2:220 < M(c)< 2:340 GeV/c2 and \sideband"

right sign pairs with 2:220 < M(c)< 2:250 GeV/c2 or 2:310 < M(c)< 2:340 GeV/c2.

The resulting proper time distributions, shown in Figs. 8b and 8d, were tted with the same technique as that used for the study of the ` channel. In the likelihood function, the signal fraction Fs was a function of the reconstructed c invariant mass and of the

decay channel, obtained from the plots shown in Figs. 7a-c. Its average value over the whole signal sample was (6910)%. The result was:

(b-baryon)= 1:19+0:21_{0:18 ps}

where the error re ects the statistical contribution only. The t gave a ying background lifetime of 1:72+0:16_{0:14 ps and a correlation coecient with the b-baryon lifetime of -0.19.}

The dierent contributions to the systematic error are shown in Table 4. The rst came from the uncertainty on the signal purity, which was varied in the t within its statistical error. The i parametrisation was studied in the simulation, following the

procedure discussed in Sect. 5.1, and a total systematic error of 0.04 ps was assigned. The error scaling factor was 1.3 in this case. A t to about 400 reconstructed b-baryon decays from a dedicated simulation sample of 20000 b ! cl(c ! pK) decays

Table 4: Contributions to the systematic error on the averageb-baryon lifetime measured using c` correlations.

Error source Range of Variation Syst. error (ps) Signal Fraction Fs 0:690:10 0:02

i Parametrisation see text 0:04

Fit procedure bias see text 0:05

< Eb > and Mbar see table 2

0:01

(!) = exp[aIW(1 !)] aIW = 1:7+3:31:7 0:01

Br(b !c`n)=Br(b !c`) 0!0:3 0:04

Total systematic error +0:07_0:08

be a systematic error from the possible bias introduced by the tting procedure. The determination of the other entries of Table 4 also followed the discussion in Sect. 5.1 closely. The eect of the b polarisation was studied in the simulation and found to be

negligible.

Summing the systematic uncertainties in quadrature gave an overall systematic un-certainty of +0:07_{0:08 ps.}

7 Conclusions

The average lifetime of the b-baryon was studied using two dierent decay channels, relying on the detection of a fast  or a c in the same jet as a high pT lepton. The

following results were obtained :

(b-baryon) = (1:46+0:22+0:07_{0:21 0:09) ps (206 ` decay vertices),}

(b-baryon) = (1:10+0:19+0:09_{0:17 0:09) ps (441  pairs),}

(b-baryon) = (1:19+0:21+0:07_{0:18 0:08) ps (125 c` decay vertices).}

The statistical correlation between the rst two analyses (20% of the  pairs used in the impact parameter measurement were already used in the  vertex measurement) and between the l and cl lepton samples (5%) was taken into account when averaging

the results. The full correlation of the entries in the lower halves of Tables 2, 3 and 4 was also taken into account in combining the systematic errors. The combined result was :

(b-baryon) = (1:25+0:13_0:11(stat)

0:04(syst)

+0:03_{0:05(syst)) ps.}

The rst systematic error resulted from the uncorrelated part of the systematic errors of the individual measurements, mainly due to experimental uncertainties. The second systematic error was due to the common uncertainty from the modelling of theb-baryon production and semi-leptonic decay.

Another measurement of theb-baryon lifetime was recently published by DELPHI [8], based on the proper decay time distribution of candidate vertices with a high momentum proton and a highpT muon:

The overlap between this sample and those used in the present work is negligible. Only a small fraction (0.02 ps) of the systematic error is correlated with the errors of the analyses reported in this paper. Combining this measurement with those presented here gives:

(b-baryon) = (1:250:110:05) ps.

This result for the averageb-baryon lifetimeincludes and therefore supersedes all previous Delphi measurements [4,8].

Acknowledgements

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Figure 2:  candidate mass distributions for reconstructed ` vertices of a) right sign and c) wrong sign respectively. b) The lifetime distribution for 206 b-baryon candidates, i.e. right sign ` vertices with 1:106 < M(p) < 1:130 GeV/c2 _{(shaded area in the}

a) M(pπ ) (GeV/c2) Entries/(4 MeV/c 2 ) b) M(pπ ) (GeV/c2) Entries/(4 MeV/c 2 ) 0 20 40 60 80 100 120 140 160 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 0 20 40 60 80 100 120 140 160 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18

• a) Data Background δ (cm) Entries/(0.01 cm) • b) Data Λ_b0_→Λ0_µ -Background δ (cm) Entries/(0.01 cm) 0 2000 4000 6000 8000 10000 12000 14000 -0.2 -0.1 0 0.1 0.2 0.3 0 20 40 60 80 100 120 -0.2 -0.1 0 0.1 0.2 0.3

Figure 7: Invariant mass distributions for right sign (full line) and wrong sign (dashed line) c candidates correlated with a high pT lepton: a) pK channel, b) pK0 channel,

Figure 8: Reconstructed cinvariant mass distribution for cvertex candidates correlated

with a high pT lepton of a) right sign and c) wrong sign; b) lifetime distribution for

b-baryon candidates, 125 right sign c` vertices with 2:250 < M(c) < 2:310 GeV/c2

(shaded area in the right sign mass plot). The full lines show the t described in the text, the dashed line is the estimated b-baryon contribution, the dotted and dot-dashed lines are the ying and non- ying backgrounds determined from d) the lifetime distribution of the 139 c` vertices in the background sample taken from the regions in a) and c) marked